Производная (sin(2*(x)))^(cot(2*x))

Вы ввели

   cot(2*x)     
sin        (2*x)

$$\sin^{\cot{\left (2 x \right )}}{\left (2 x \right )}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(\log{\left (\cot{\left (2 x \right )} \right )} + 1\right) \cot^{\cot{\left (2 x \right )}}{\left (2 x \right )}$

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Ответ:

$\left(\log{\left (\cot{\left (2 x \right )} \right )} + 1\right) \cot^{\cot{\left (2 x \right )}}{\left (2 x \right )}$

Первая производная

   cot(2*x)      //          2     \                 2*cos(2*x)*cot(2*x)\
sin        (2*x)*|\-2 - 2*cot (2*x)/*log(sin(2*x)) + -------------------|
                 \                                         sin(2*x)     /

$$\left(\left(- 2 \cot^{2}{\left (2 x \right )} - 2\right) \log{\left (\sin{\left (2 x \right )} \right )} + \frac{2 \cos{\left (2 x \right )}}{\sin{\left (2 x \right )}} \cot{\left (2 x \right )}\right) \sin^{\cot{\left (2 x \right )}}{\left (2 x \right )}$$

Вторая производная

                   /                                                   2                 2                   /       2     \                                                    \
     cot(2*x)      |//       2     \                 cos(2*x)*cot(2*x)\               cos (2*x)*cot(2*x)   2*\1 + cot (2*x)/*cos(2*x)     /       2     \                       |
4*sin        (2*x)*||\1 + cot (2*x)/*log(sin(2*x)) - -----------------|  - cot(2*x) - ------------------ - -------------------------- + 2*\1 + cot (2*x)/*cot(2*x)*log(sin(2*x))|
                   |\                                     sin(2*x)    /                      2                      sin(2*x)                                                    |
                   \                                                                      sin (2*x)                                                                             /

$$4 \left(\left(\left(\cot^{2}{\left (2 x \right )} + 1\right) \log{\left (\sin{\left (2 x \right )} \right )} - \frac{\cos{\left (2 x \right )} \cot{\left (2 x \right )}}{\sin{\left (2 x \right )}}\right)^{2} + 2 \left(\cot^{2}{\left (2 x \right )} + 1\right) \log{\left (\sin{\left (2 x \right )} \right )} \cot{\left (2 x \right )} - \frac{2 \cos{\left (2 x \right )}}{\sin{\left (2 x \right )}} \left(\cot^{2}{\left (2 x \right )} + 1\right) - \cot{\left (2 x \right )} - \frac{\cos^{2}{\left (2 x \right )} \cot{\left (2 x \right )}}{\sin^{2}{\left (2 x \right )}}\right) \sin^{\cot{\left (2 x \right )}}{\left (2 x \right )}$$